Question

The probability of winning a match for team a is 0.6. find the probability of winning 3 matches out of 5.

Answer 1

The probability is 0.3456

Given:

Probability = 0.6

Step-by-step explanation:

The probability of losing a game is 1 - 0.6 = 0.4

Thus, using the relation of probabilities of winning and losing we have the probability of winning exactly 3 games out of the 5 games is,

$(0.6)^{3} \times(0.4)^{2}=0.03456$

However, such an incident can occur in $\begin{array}{l}{5} \\ {3}\end{array} C$ ways.  

These number of events are given as:

$\Rightarrow \frac{5 !}{3 ! \times 2 !}$

Which gives us: 10 ways

Thus, the overall probability of winning three out of five matches is 10 \times 0.03456

Which results in 0.3456